The results of the distribution of values hardness cylindrical shell shell steel structures 20, subject to cyclic loading by internal pressure, contributing to the emergence of a structural material elastic-plastic deformations. The results of measuring the hardness of the material processed by the method of the multifractal parameterization and analyzed changes in the level of fatigue damage accumulation. Calculation of multifractal characteristics was performed using the product program MFDrom, developed by professor G.V. Vstovski that allows the conversion of the results of hardness measurement data in mathematical form and maintain a computer analysis of the distribution of hardness values, perform a quantitative description of the degree of violation of fractal symmetry. It was found that the level of fatigue damage accumulation Ni/Np = 0.76 ± 0.05 hidden orderly structure (D1-D40) and the degree of homogeneity (F40) reaches a minimum value, and the fractal dimension (D0) is characterized by a maximum value. This is because when the material limit state is a change adaptation mechanism structure to external influence. Analysis of changes in the values of hardness of the shell structure of the level of accumulated fatigue damage has shown that during operation there is a general tendency of decrease in hardness values cylindrical shell. The material of construction of the shell structure of steel 20 as a result of cyclic loading internal pressure softens. Set point depending on the change of the structure of the mechanism of adaptation to external influences, in which the structural material reaches a limiting condition, and can be used to determine the period of safe operation of shell structures subjected to cyclic loading.